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A pairwise interaction theory for determining the linear acoustic properties of dilute bubbly liquids

Published online by Cambridge University Press:  26 April 2006

A. S. Sangani
A. S. Sangani
Affiliation:
Department of Chemical Engineering, Syracuse University, Syracuse, NY 13244, USA
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Abstract

The problem of determining the acoustic properties of dilute bubbly liquids is examined using the method of ensemble-averaged equations and pairwise interactions. The phase speed and attenuation of sound waves in the small-amplitude regime are determined as a function of frequency of sound waves including the effects of finite surface tension, small viscosity of the liquid, and non-adiabatic thermal changes, and compared with the experimental data available in the literature. An excellent agreement is found for frequencies smaller than about 1.3 times the natural frequency of the bubbles, but the discrepancy is substantial at larger frequencies.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 232 , November 1991 , pp. 221 - 284
Copyright
© 1991 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards.
Acrivos, A. & Chang, E. Y. 1986 The transport properties of non-dilute suspensions. Renormalization via an effective continuum method. In Physics and Chemistry of Porous Media, AIP Conf. Proc. (ed. J. R. Banavar, J. Koplik & K. W. Winkler), vol. 154, p. 129.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Batchelor, G. K. 1969 Compression waves in a suspension of gas bubbles in liquid. Fluid Dyn. Trans. 4, 425.Google Scholar
Batchelor, G. K. 1974 Transport properties of two-phase materials with random structure. Ann. Rev. Fluid Mech. 6, 227.Google Scholar
Biesheuvel, A. & Spoelstra, S. 1989 The added mass coefficient of a dispersion of spherical gas bubbles in liquid. Intl J. Multiphase Flow 15, 911.Google Scholar
Biesheuvel, A. & Wijngaarden, L. Van 1984 Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. J. Fluid Mech. 148, 301.Google Scholar
Caflisch, R. E., Miksis, M. J., Papanicolaou, G. C. & Ting, L. 1985a Effective equation for wave propagation in bubbly liquids. J. Fluid Mech. 153, 259.Google Scholar
Caflisch, R. E., Miksis, M. J., Papanicolaou, G. C. & Ting, L. 1985b Wave propagation in bubbly liquids at finite volume fraction. J. Fluid Mech. 160, 1.Google Scholar
Carstensen, E. L. & Foldy, L. L. 1947 Propagation of sound through a liquid containing bubbles. J. Acoust. Soc. Am. 19, 481.Google Scholar
Commander, K. W. & Prosperetti, A. 1989 Linear pressure waves in bubbly liquids: Comparison between theory and experiments. J. Acoust. Soc. Am. 85, 732.Google Scholar
Foldy, L. L. 1945 The multiple scattering of waves. Phys. Rev. 67, 107.Google Scholar
Fox, F. E., Curley, S. R. & Larson, G. S. 1955 Phase velocity and absorption measurements in water containing air bubbles. J. Acoust. Soc. Am. 27, 534.Google Scholar
Hinch, E. J. 1977 An averaged-equation approach to particle interactions in a fluid suspension. J. Fluid Mech. 83, 695.Google Scholar
Hobsons, E. W. 1931 The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press.
Howblls, I. D. 1974 Drag due to the motion of a Newtonian fluid through a sparse random array of small fixed rigid objects. J. Fluid Mech. 64, 449.Google Scholar
Jeffrey, D. J. 1973 Conduction through a random suspension of spheres. Proc. R. Soc. Land. A 335, 355.Google Scholar
Kang, I. S. & Leal, L. G. 1988 Small-amplitude perturbations of shape for a nearly spherical bubble in an inviscid straining flow (steady shapes and oscillatory motion). J. Fluid Mech. 187, 231.Google Scholar
Kim, S. & Russel, W. B. 1985a The hydrodynamic interactions between two spheres in a Brinkman medium. J. Fluid Mech. 154, 253.Google Scholar
Kim, S. & Russel, W. B. 1985b Modelling of porous media by renormalization of the Stokes equations. J. Fluid Mech. 154, 269.Google Scholar
Koch, d. L. & Brady, J. F. 1987 A non-local description of advection-diffusion with application to dispersion in porous media. J. Fluid Mech. 180, 387.Google Scholar
Kol'tsova, I. S., Krynskii, L. O., Mikhalov, I. G. & Pokrovskaya, I. E. 1979 Attenuation of ultrasonic waves in low-viscosity liquids containing gas bubbles. Akust. Zh. 25, 725. (English transl: Sov. Phys. Acoust. 25, 409.)Google Scholar
Levich, V. G. 1962 Physico-Chemical Hydrodynamics. Prentice Hall.
Micaelli, J.-C. 1982 Propagation d'ondes dans les écoulements diphasiques a bulles a deux constituants. Etude théorique et expérimentale. Thèse, Université de Grenoble.
Miksis, M. J. & Ting, L. 1986 Wave propagation in a bubbly liquid with finite-amplitude asymmetric bubble oscillations. Phys. Fluids 29, 603.Google Scholar
Miksis, M. J. & Ting, L. 1987a Viscous effects on wave propagation in a bubbly liquid. Phys. Fluids 30, 1683.Google Scholar
Miksis, M. J. & Ting, L. 1987b Wave propagation in a multiphase media with viscous and thermal effects. ANS Proc. Natl Heat Transfer Conf., p. 145.
Prosperetti, A. 1984 Bubble phenomena in sound fields: part one. Ultrasonics 22, 69.Google Scholar
Prosperetti, A. & Kim, D. H. 1989 Pressure waves in bubbly liquids at small gas volume fractions. In Fundamentals of Gas and Liquid Flows (ed. E. E. Michaelides & M. P. Sharma), p. 19. ASME.
Prosperetti, A. & Lezzi, A. 1986 Bubble dynamics in a compressible liquids. Part 1. First-order theory. J. Fluid Mech. 168, 457.Google Scholar
Rubinstein, J. 1985 Bubble interaction effects on waves in bubbly liquids. J. Acoust. Am. 77, 2061.Google Scholar
Ruggles, A. E., Scarton, H. A. & Lahey, R. T. 1986 An investigation of the propagation of pressure perturbations in bubbly air/water flows. First Intl Multiphase Fluids Transients Symp. (ed. H. H. Safwat, J. Braun & U. S. Rohatgi). ASME.
Sangani, A. S. & Yao, C. 1988 Bulk conductivity of composites with spherical inclusions. J. Appl. Phys. 63, 1334.Google Scholar
Sangani, A. S., Zhang, D. & Prosperetti, A. 1991 The added mass, Basset, and viscous drag coefficients in non-dilute bubbly liquids undergoing small amplitude oscillatory motion. Phys. Fluids (submitted).Google Scholar
Scott, J. F. 1981 Singular perturbation applied to the collective oscillation of gas bubbles in a liquid. J. Fluid Mech. 113, 487.Google Scholar
Shaqfeh, E. 1988 A nonlocal theory for the heat transport in composites containing highly conducting fibrous inclusions. Phys. Fluids 31, 2405.Google Scholar
Silberman, E. 1957 Sound velocity and attenuation in bubbly mixtures measured in standing wave tubes. J. Acoust. Soc. Am. 29, 925.Google Scholar
Twerski, V. 1962 On scattering of waves by random distributions. I. Free-space scatterer formalism. J. Math. Phys. 3, 700.Google Scholar
Wijngaarden, L. Van 1972 One-dimensional flow of liquids containing small bubbles. Ann. Rev. Fluid Mech. 4, 369.Google Scholar
Wijngaarden, L. Van 1976 Hydrodynamic interaction between bubbles in liquid. J. Fluid Mech. 77, 24.Google Scholar